JEE Main 2024 (Online) 5th April Morning Shift

Given below are two statement :
Statements I : Bromination of phenol in solvent with low polarity such as \(\mathrm{CHCl}_3\) or \(\mathrm{CS}_2\) requires Lewis acid catalyst.
Statements II : The Lewis acid catalyst polarises the bromine t...

For the Compounds :
(A) \(\mathrm{H}_3 \mathrm{C}-\mathrm{CH}_2-\mathrm{O}-\mathrm{CH}_2-\mathrm{CH}_2-\mathrm{CH}_3\)
(B) \(\mathrm{H}_3 \mathrm{C}-\mathrm{CH}_2-\mathrm{CH}_2-\mathrm{CH}_2-\mathrm{CH}_3\)
(C)
(D)
The increasing order of...

Consider the given chemical reaction sequence :

Total sum of oxygen atoms in Product A and Product B are ________.

Identify 'A' in the following reaction :

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : Cis form of alkene is found to be more polar than the trans form.
Reason (R) : Dipole moment of trans isomer of 2-but...

Which of the following gives a positive test with ninhydrin ?

In the lewis dot structure for \(\mathrm{NO}_2^{-}\), total number of valence electrons around nitrogen is _________.

Number of \(\sigma\) and \(\pi\) bonds present in ethylene molecule is respectively :

The following reaction occurs in the Blast furnance where iron ore is reduced to iron metal
\(\mathrm{Fe}_2 \mathrm{O}_{3(s)}+3 \mathrm{CO}_{(g)} \rightleftharpoons \mathrm{Fe}_{(\mathrm{l})}+3 \mathrm{CO}_{2(g)}\)
Using the Le-chatelier's ...

During Kinetic study of reaction \(\mathrm{2 A+B \rightarrow C+D}\), the following results were obtained :

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\(9.3 \mathrm{~g}\) of pure aniline is treated with bromine water at room temperature to give a white precipitate of the product '\(\mathrm{P}\)'. The mass of product '\(\mathrm{P}\)' obtained is \(26.4 \mathrm{~g}\). The percentage yield i...

Identify compound (Z) in the following reaction sequence.

Which one of the following complexes will exhibit the least paramagnetic behaviour ?
[Atomic number, \(\mathrm{Cr}=24, \mathrm{Mn}=25, \mathrm{Fe}=26, \mathrm{Co}=27\)]

The spin-only magnetic moment value of the ion among \(\mathrm{Ti}^{2+}, \mathrm{V}^{2+}, \mathrm{Co}^{3+}\) and \(\mathrm{Cr}^{2+}\), that acts as strong oxidising agent in aqueous solution is _________ BM (Near integer).
(Given atomic num...

The correct order of ligands arranged in increasing field strength.

The metal that shows highest and maximum number of oxidation state is :

In a borax bead test under hot condition, a metal salt (one from the given) is heated at point B of the flame, resulted in green colour salt bead. The spin-only magnetic moment value of the salt is _______ BM (Nearest integer) [Given atomi...

The reaction at cathode in the cells commonly used in clocks involves.

Molar ionic conductivities of divalent cation and anion are \(57 \mathrm{~S~cm}^2 \mathrm{~mol}^{-1}\) and \(73 \mathrm{~S~cm}^2 \mathrm{~mol}^{-1}\) respectively. The molar conductivity of solution of an electrolyte with the above cation a...

The number of halobenzenes from the following that can be prepared by Sandmeyer's reaction is _________

Given below are two statements :
Statement I :
Nitration of benzene involves the following step -

Statement II : Use of Lewis base promotes the electrophilic substitution of benzene.
In the light of the above statements, choose the most ap...

The number of neutrons present in the more abundant isotope of boron is '\(x\)'. Amorphous boron upon heating with air forms a product, in which the oxidation state of boron is '\(y\)'. The value of \(x+y\) is _________ .

The statement(s) that are correct about the species \(\mathrm{O}^{2-}, \mathrm{F}^{-}, \mathrm{Na}^{+}\) and \(\mathrm{Mg}^{2+}\).
(A) All are isoelectronic
(B) All have the same nuclear charge
(C) \(\mathrm{O}^{2-}\) has the largest ionic ...

Given below are two statements:
Statement I: In group 13, the stability of +1 oxidation state increases down the group.
Statement II : The atomic size of gallium is greater than that of aluminium.
In the light of the above statements, choos...

An artificial cell is made by encapsulating \(0.2 \mathrm{~M}\) glucose solution within a semipermeable membrane. The osmotic pressure developed when the artificial cell is placed within a \(0.05 \mathrm{~M}\) solution of \(\mathrm{NaCl}\) ...

An organic compound has \(42.1 \%\) carbon, \(6.4 \%\) hydrogen and remainder is oxygen. If its molecular weight is 342 , then its molecular formula is :

The incorrect postulates of the Dalton's atomic theory are :
(A) Atoms of different elements differ in mass.
(B) Matter consists of divisible atoms.
(C) Compounds are formed when atoms of different element combine in a fixed ratio.
(D) All ...

The value of Rydberg constant \((R_H)\) is \(2.18 \times 10^{-18} \mathrm{~J}\). The velocity of electron having mass \(9.1 \times 10^{-31} \mathrm{~kg}\) in Bohr's first orbit of hydrogen atom = ________ \(\times 10^5 \mathrm{~ms}^{-1}\) (...

The heat of combustion of solid benzoic acid at constant volume is \(-321.30 \mathrm{~kJ}\) at \(27^{\circ} \mathrm{C}\). The heat of combustion at constant pressure is \((-321.30-x \mathrm{R}) \mathrm{~kJ}\), the value of \(x\) is ________...

Given below are two statements: One is labelled as Assertion (A) and the other is labelled as Reason (R)
Assertion (A) : Enthalpy of neutralisation of strong monobasic acid with strong monoacidic base is always $$-57 \mathrm{~kJ} \mathrm{~m...

Let \(\mathrm{d}\) be the distance of the point of intersection of the lines \(\frac{x+6}{3}=\frac{y}{2}=\frac{z+1}{1}\) and \(\frac{x-7}{4}=\frac{y-9}{3}=\frac{z-4}{2}\) from the point \((7,8,9)\). Then \(\mathrm{d}^2+6\) is equal to :

If the line \(\frac{2-x}{3}=\frac{3 y-2}{4 \lambda+1}=4-z\) makes a right angle with the line \(\frac{x+3}{3 \mu}=\frac{1-2 y}{6}=\frac{5-z}{7}\), then \(4 \lambda+9 \mu\) is equal to :

For the function
\(f(x)=\sin x+3 x-\frac{2}{\pi}\left(x^2+x\right), \text { where } x \in\left[0, \frac{\pi}{2}\right],\)
consider the following two statements :
(I) \(f\) is increasing in \(\left(0, \frac{\pi}{2}\right)\).
(II) $$f^{\prime...

Let a rectangle ABCD of sides 2 and 4 be inscribed in another rectangle PQRS such that the vertices of the rectangle ABCD lie on the sides of the rectangle PQRS. Let a and b be the sides of the rectangle PQRS when its area is maximum. Then ...

Let \(f(x)=x^5+2 x^3+3 x+1, x \in \mathbf{R}\), and \(g(x)\) be a function such that \(g(f(x))=x\) for all \(x \in \mathbf{R}\). Then \(\frac{g(7)}{g^{\prime}(7)}\) is equal to :

The area of the region enclosed by the parabolas \(y=x^2-5 x\) and \(y=7 x-x^2\) is ________.

If the constant term in the expansion of \(\left(1+2 x-3 x^3\right)\left(\frac{3}{2} x^2-\frac{1}{3 x}\right)^9\) is \(\mathrm{p}\), then \(108 \mathrm{p}\) is equal to ________.

Let a circle C of radius 1 and closer to the origin be such that the lines passing through the point \((3,2)\) and parallel to the coordinate axes touch it. Then the shortest distance of the circle C from the point \((5,5)\) is :

Consider the following two statements :
Statement I: For any two non-zero complex numbers $$z_1, z_2,(|z_1|+|z_2|)\left|\frac{z_1}{\left|z_1\right|}+\frac{z_2}{\left|z_2\right|}\right| \leq 2\left(\left|z_1\right|+\left|z_2\right|\right) \t...

The value of \(\int_\limits{-\pi}^\pi \frac{2 y(1+\sin y)}{1+\cos ^2 y} d y\) is :

The integral \(\int_\limits0^{\pi / 4} \frac{136 \sin x}{3 \sin x+5 \cos x} \mathrm{~d} x\) is equal to :

If \(y=y(x)\) is the solution of the differential equation \(\frac{\mathrm{d} y}{\mathrm{~d} x}+2 y=\sin (2 x), y(0)=\frac{3}{4}\), then \(y\left(\frac{\pi}{8}\right)\) is equal to :

Let the line \(2 x+3 y-\mathrm{k}=0, \mathrm{k}>0\), intersect the \(x\)-axis and \(y\)-axis at the points \(\mathrm{A}\) and \(\mathrm{B}\), respectively. If the equation of the circle having the line segment \(A B\) as a diameter is $$x^2...

If \(S=\{a \in \mathbf{R}:|2 a-1|=3[a]+2\{a \}\}\), where \([t]\) denotes the greatest integer less than or equal to \(t\) and \(\{t\}\) represents the fractional part of \(t\), then \(72 \sum_\limits{a \in S} a\) is equal to _________.

Let \(A=\{1,3,7,9,11\}\) and \(B=\{2,4,5,7,8,10,12\}\). Then the total number of one-one maps \(f: A \rightarrow B\), such that \(f(1)+f(3)=14\), is :

If the function \(f(x)=\frac{\sin 3 x+\alpha \sin x-\beta \cos 3 x}{x^3}, x \in \mathbf{R}\), is continuous at \(x=0\), then \(f(0)\) is equal to :

Let \(f\) be a differentiable function in the interval \((0, \infty)\) such that \(f(1)=1\) and \(\lim _\limits{t \rightarrow x} \frac{t^2 f(x)-x^2 f(t)}{t-x}=1\) for each \(x>0\). Then \(2 f(2)+3 f(3)\) is equal to _________.

Let A and B be two square matrices of order 3 such that \(\mathrm{|A|=3}\) and \(\mathrm{|B|=2}\). Then $$|\mathrm{A}^{\mathrm{T}} \mathrm{A}(\operatorname{adj}(2 \mathrm{~A}))^{-1}(\operatorname{adj}(4 \mathrm{~B}))(\operatorname{adj}(\mat...

If the system of equations
$$\begin{array}{r} 11 x+y+\lambda z=-5 \\ 2 x+3 y+5 z=3 \\ 8 x-19 y-39 z=\mu \end{array}$$
has infinitely many solutions, then \(\lambda^4-\mu\) is equal to :

Suppose \(\mathrm{AB}\) is a focal chord of the parabola \(y^2=12 x\) of length \(l\) and slope \(\mathrm{m}<\sqrt{3}\). If the distance of the chord \(\mathrm{AB}\) from the origin is \(\mathrm{d}\), then \(l \mathrm{~d}^2\) is equal to __...